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<div class="header">
  <div class="headertitle"><div class="title">Newton.hpp</div></div>
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<div class="contents">
<a href="_newton_8hpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno">    1</span> </div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno">   33</span><span class="preprocessor">#pragma once</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno">   34</span> </div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno">   35</span><span class="preprocessor">#include &lt;cmath&gt;</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno">   36</span><span class="preprocessor">#include &lt;functional&gt;</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno">   37</span><span class="preprocessor">#include &lt;utility&gt;</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno">   38</span> </div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno">   39</span><span class="preprocessor">#include &quot;<a class="code" href="_types_8hpp.html">NumCpp/Core/Types.hpp</a>&quot;</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno">   40</span><span class="preprocessor">#include &quot;<a class="code" href="_iteration_8hpp.html">NumCpp/Roots/Iteration.hpp</a>&quot;</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno">   41</span> </div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno">   42</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespacenc_1_1roots.html">nc::roots</a></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno">   43</span>{</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno">   44</span>    <span class="comment">//================================================================================</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno">   45</span>    <span class="comment">// Class Description:</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"><a class="line" href="classnc_1_1roots_1_1_newton.html">   48</a></span><span class="comment"></span>    <span class="keyword">class </span><a class="code hl_class" href="classnc_1_1roots_1_1_newton.html">Newton</a> : <span class="keyword">public</span> <a class="code hl_class" href="classnc_1_1roots_1_1_iteration.html">Iteration</a></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno">   49</span>    {</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno">   50</span>    <span class="keyword">public</span>:</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno">   51</span>        <span class="comment">//============================================================================</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno">   52</span>        <span class="comment">// Method Description:</span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"><a class="line" href="classnc_1_1roots_1_1_newton.html#ab5b82361c4ce325e6165e023c0255d3e">   59</a></span><span class="comment"></span>        <a class="code hl_function" href="classnc_1_1roots_1_1_newton.html#ab5b82361c4ce325e6165e023c0255d3e">Newton</a>(<span class="keyword">const</span> <span class="keywordtype">double</span> epsilon, std::function&lt;<span class="keywordtype">double</span>(<span class="keywordtype">double</span>)&gt; <a class="code hl_function" href="namespacenc_1_1random_1_1detail.html#af5bfd54c6d5d0ad7e16e6e532b0dfb2e">f</a>, std::function&lt;<span class="keywordtype">double</span>(<span class="keywordtype">double</span>)&gt; fPrime) noexcept :</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno">   60</span>            <a class="code hl_function" href="classnc_1_1roots_1_1_iteration.html#a2d7285a81c033d56ce8283b6dbfca136">Iteration</a>(epsilon),</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno">   61</span>            f_(std::move(<a class="code hl_function" href="namespacenc_1_1random_1_1detail.html#af5bfd54c6d5d0ad7e16e6e532b0dfb2e">f</a>)),</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno">   62</span>            fPrime_(std::move(fPrime))</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno">   63</span>        {</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno">   64</span>        }</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno">   65</span> </div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno">   66</span>        <span class="comment">//============================================================================</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno">   67</span>        <span class="comment">// Method Description:</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"><a class="line" href="classnc_1_1roots_1_1_newton.html#aecc72e3899f42b277536689439ea24bc">   75</a></span><span class="comment"></span>        <a class="code hl_function" href="classnc_1_1roots_1_1_newton.html#aecc72e3899f42b277536689439ea24bc">Newton</a>(<span class="keyword">const</span> <span class="keywordtype">double</span>                  epsilon,</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno">   76</span>               <span class="keyword">const</span> <a class="code hl_typedef" href="namespacenc.html#af0f49663fb63332596e2e6327009d581">uint32</a>                  maxNumIterations,</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno">   77</span>               std::function&lt;<span class="keywordtype">double</span>(<span class="keywordtype">double</span>)&gt; <a class="code hl_function" href="namespacenc_1_1random_1_1detail.html#af5bfd54c6d5d0ad7e16e6e532b0dfb2e">f</a>,</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno">   78</span>               std::function&lt;<span class="keywordtype">double</span>(<span class="keywordtype">double</span>)&gt; fPrime) noexcept :</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno">   79</span>            <a class="code hl_function" href="classnc_1_1roots_1_1_iteration.html#a2d7285a81c033d56ce8283b6dbfca136">Iteration</a>(epsilon, maxNumIterations),</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno">   80</span>            f_(std::move(<a class="code hl_function" href="namespacenc_1_1random_1_1detail.html#af5bfd54c6d5d0ad7e16e6e532b0dfb2e">f</a>)),</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno">   81</span>            fPrime_(std::move(fPrime))</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno">   82</span>        {</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno">   83</span>        }</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno">   84</span> </div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno">   85</span>        <span class="comment">//============================================================================</span></div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno">   86</span>        <span class="comment">// Method Description:</span></div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"><a class="line" href="classnc_1_1roots_1_1_newton.html#a25702b087e2e9917af0c31fe1dbdf442">   89</a></span><span class="comment"></span>        <a class="code hl_function" href="classnc_1_1roots_1_1_newton.html#a25702b087e2e9917af0c31fe1dbdf442">~Newton</a>() noexcept override = default;</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno">   90</span> </div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno">   91</span>        <span class="comment">//============================================================================</span></div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno">   92</span>        <span class="comment">// Method Description:</span></div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"><a class="line" href="classnc_1_1roots_1_1_newton.html#aaed2535d1abdb0c6790aea60762ed789">   98</a></span><span class="comment"></span>        <span class="keywordtype">double</span> <a class="code hl_function" href="classnc_1_1roots_1_1_newton.html#aaed2535d1abdb0c6790aea60762ed789">solve</a>(<span class="keywordtype">double</span> x)</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno">   99</span>        {</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno">  100</span>            <a class="code hl_function" href="classnc_1_1roots_1_1_iteration.html#a85e79a4794bc3a6ac6bc3564956737a2">resetNumberOfIterations</a>();</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno">  101</span> </div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno">  102</span>            <span class="keywordtype">double</span> fx      = f_(x);</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno">  103</span>            <span class="keywordtype">double</span> fxPrime = fPrime_(x);</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno">  104</span> </div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno">  105</span>            <span class="keywordflow">while</span> (std::fabs(fx) &gt;= <a class="code hl_variable" href="classnc_1_1roots_1_1_iteration.html#a5eafe219bb90f82da4ece84f012a411a">epsilon_</a>)</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno">  106</span>            {</div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno">  107</span>                x = calculateX(x, fx, fxPrime);</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno">  108</span> </div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno">  109</span>                fx      = f_(x);</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno">  110</span>                fxPrime = fPrime_(x);</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno">  111</span> </div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno">  112</span>                <a class="code hl_function" href="classnc_1_1roots_1_1_iteration.html#ad0262a1a694e734ebc154c77f010bcff">incrementNumberOfIterations</a>();</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno">  113</span>            }</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno">  114</span> </div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno">  115</span>            <span class="keywordflow">return</span> x;</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno">  116</span>        }</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno">  117</span> </div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno">  118</span>    <span class="keyword">private</span>:</div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno">  119</span>        <span class="comment">//============================================================================</span></div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno">  120</span>        <span class="keyword">const</span> std::function&lt;double(<span class="keywordtype">double</span>)&gt; f_;</div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno">  121</span>        <span class="keyword">const</span> std::function&lt;double(<span class="keywordtype">double</span>)&gt; fPrime_;</div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno">  122</span> </div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno">  123</span>        <span class="comment">//============================================================================</span></div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno">  124</span>        <span class="comment">// Method Description:</span></div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno">  132</span><span class="comment"></span>        <span class="keyword">static</span> <span class="keywordtype">double</span> calculateX(<span class="keywordtype">double</span> x, <span class="keywordtype">double</span> fx, <span class="keywordtype">double</span> fxPrime) <span class="keyword">noexcept</span></div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno">  133</span>        {</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno">  134</span>            <span class="keywordflow">return</span> x - fx / fxPrime;</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno">  135</span>        }</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno">  136</span>    };</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno">  137</span>} <span class="comment">// namespace nc::roots</span></div>
<div class="ttc" id="a_iteration_8hpp_html"><div class="ttname"><a href="_iteration_8hpp.html">Iteration.hpp</a></div></div>
<div class="ttc" id="a_types_8hpp_html"><div class="ttname"><a href="_types_8hpp.html">Types.hpp</a></div></div>
<div class="ttc" id="aclassnc_1_1roots_1_1_iteration_html"><div class="ttname"><a href="classnc_1_1roots_1_1_iteration.html">nc::roots::Iteration</a></div><div class="ttdoc">ABC for iteration classes to derive from.</div><div class="ttdef"><b>Definition:</b> Iteration.hpp:46</div></div>
<div class="ttc" id="aclassnc_1_1roots_1_1_iteration_html_a2d7285a81c033d56ce8283b6dbfca136"><div class="ttname"><a href="classnc_1_1roots_1_1_iteration.html#a2d7285a81c033d56ce8283b6dbfca136">nc::roots::Iteration::Iteration</a></div><div class="ttdeci">Iteration(double epsilon) noexcept</div><div class="ttdef"><b>Definition:</b> Iteration.hpp:54</div></div>
<div class="ttc" id="aclassnc_1_1roots_1_1_iteration_html_a5eafe219bb90f82da4ece84f012a411a"><div class="ttname"><a href="classnc_1_1roots_1_1_iteration.html#a5eafe219bb90f82da4ece84f012a411a">nc::roots::Iteration::epsilon_</a></div><div class="ttdeci">const double epsilon_</div><div class="ttdef"><b>Definition:</b> Iteration.hpp:114</div></div>
<div class="ttc" id="aclassnc_1_1roots_1_1_iteration_html_a85e79a4794bc3a6ac6bc3564956737a2"><div class="ttname"><a href="classnc_1_1roots_1_1_iteration.html#a85e79a4794bc3a6ac6bc3564956737a2">nc::roots::Iteration::resetNumberOfIterations</a></div><div class="ttdeci">void resetNumberOfIterations() noexcept</div><div class="ttdef"><b>Definition:</b> Iteration.hpp:94</div></div>
<div class="ttc" id="aclassnc_1_1roots_1_1_iteration_html_ad0262a1a694e734ebc154c77f010bcff"><div class="ttname"><a href="classnc_1_1roots_1_1_iteration.html#ad0262a1a694e734ebc154c77f010bcff">nc::roots::Iteration::incrementNumberOfIterations</a></div><div class="ttdeci">void incrementNumberOfIterations()</div><div class="ttdef"><b>Definition:</b> Iteration.hpp:103</div></div>
<div class="ttc" id="aclassnc_1_1roots_1_1_newton_html"><div class="ttname"><a href="classnc_1_1roots_1_1_newton.html">nc::roots::Newton</a></div><div class="ttdef"><b>Definition:</b> Newton.hpp:49</div></div>
<div class="ttc" id="aclassnc_1_1roots_1_1_newton_html_a25702b087e2e9917af0c31fe1dbdf442"><div class="ttname"><a href="classnc_1_1roots_1_1_newton.html#a25702b087e2e9917af0c31fe1dbdf442">nc::roots::Newton::~Newton</a></div><div class="ttdeci">~Newton() noexcept override=default</div></div>
<div class="ttc" id="aclassnc_1_1roots_1_1_newton_html_aaed2535d1abdb0c6790aea60762ed789"><div class="ttname"><a href="classnc_1_1roots_1_1_newton.html#aaed2535d1abdb0c6790aea60762ed789">nc::roots::Newton::solve</a></div><div class="ttdeci">double solve(double x)</div><div class="ttdef"><b>Definition:</b> Newton.hpp:98</div></div>
<div class="ttc" id="aclassnc_1_1roots_1_1_newton_html_ab5b82361c4ce325e6165e023c0255d3e"><div class="ttname"><a href="classnc_1_1roots_1_1_newton.html#ab5b82361c4ce325e6165e023c0255d3e">nc::roots::Newton::Newton</a></div><div class="ttdeci">Newton(const double epsilon, std::function&lt; double(double)&gt; f, std::function&lt; double(double)&gt; fPrime) noexcept</div><div class="ttdef"><b>Definition:</b> Newton.hpp:59</div></div>
<div class="ttc" id="aclassnc_1_1roots_1_1_newton_html_aecc72e3899f42b277536689439ea24bc"><div class="ttname"><a href="classnc_1_1roots_1_1_newton.html#aecc72e3899f42b277536689439ea24bc">nc::roots::Newton::Newton</a></div><div class="ttdeci">Newton(const double epsilon, const uint32 maxNumIterations, std::function&lt; double(double)&gt; f, std::function&lt; double(double)&gt; fPrime) noexcept</div><div class="ttdef"><b>Definition:</b> Newton.hpp:75</div></div>
<div class="ttc" id="anamespacenc_1_1random_1_1detail_html_af5bfd54c6d5d0ad7e16e6e532b0dfb2e"><div class="ttname"><a href="namespacenc_1_1random_1_1detail.html#af5bfd54c6d5d0ad7e16e6e532b0dfb2e">nc::random::detail::f</a></div><div class="ttdeci">dtype f(GeneratorType &amp;generator, dtype inDofN, dtype inDofD)</div><div class="ttdef"><b>Definition:</b> f.hpp:56</div></div>
<div class="ttc" id="anamespacenc_1_1roots_html"><div class="ttname"><a href="namespacenc_1_1roots.html">nc::roots</a></div><div class="ttdef"><b>Definition:</b> Bisection.hpp:43</div></div>
<div class="ttc" id="anamespacenc_html_af0f49663fb63332596e2e6327009d581"><div class="ttname"><a href="namespacenc.html#af0f49663fb63332596e2e6327009d581">nc::uint32</a></div><div class="ttdeci">std::uint32_t uint32</div><div class="ttdef"><b>Definition:</b> Types.hpp:40</div></div>
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